Evolution of Spacetime arises due to the departure from Holographic Equipartition in all Lanczos-Lovelock Theories of Gravity

TL;DR

This paper extends the thermodynamic interpretation of spacetime evolution, originally in general relativity, to all Lanczos-Lovelock gravity theories, showing that their dynamics can be understood through surface and bulk degrees of freedom and holographic equipartition.

Contribution

It generalizes the thermodynamic description of spacetime evolution to Lanczos-Lovelock models, linking Noether charge, Wald entropy, and degrees of freedom to holographic principles.

Findings

The Noether charge equals the boundary heat content in Lanczos-Lovelock gravity.

Spacetime evolution is driven by the difference between surface and bulk degrees of freedom.

Holographic equipartition holds when the spacetime foliation is time-independent.

Abstract

In the case of general relativity one can interpret the Noether charge in any bulk region as the heat content $TS$ of its boundary surface. Further, the time evolution of spacetime metric in Einstein's theory arises due to the difference $(N_{sur}-N_{bulk})$ of suitably defined surface and bulk degrees of freedom. We show that this thermodynamic interpretation generalizes in a natural fashion to all Lanczos-Lovelock models of gravity. The Noether charge, related to time evolution vector field, in a bulk region of space is equal to the heat content $TS$ of the boundary surface with the temperature $T$ defined using local Rindler observers and $S$ being the Wald entropy. Using the Wald entropy to define the surface degrees of freedom $N_{sur}$ and Komar energy density to define the bulk degrees of freedom $N_{bulk}$, we can also show that the time evolution of the geometry is sourced by $(N_{sur}-N_{bulk})$. When it is possible to choose the foliation of spacetime such that metric is independent of time, the above dynamical equation yields the holographic equipartition for Lanczos-Lovelock gravity with $N_{sur}=N_{bulk}$. The implications are discussed.